AN INTERPOLATION APPROACH TO L∞ A PRIORI ESTIMATES FOR ELLIPTIC PROBLEMS WITH NONLINEARITY ON THE BOUNDARY

被引：0

作者：

Chhetri, Maya ^{[1
]}

Mavinga, Nsoki ^{[2
]}

Pardo, Rosa ^{[3
]}

机构：

[1] Univ North Carolina Greensboro, Dept Math & Stat, Greensboro, NC 27402 USA

[2] Swarthmore Coll, Dept Math & Stat, Swarthmore, PA 19081 USA

[3] Univ Complutense Madrid, Dept Math Anal & Appl Math, Madrid 28040, Spain

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2025年 / 153卷 / 04期

基金：

美国国家科学基金会;

关键词：

Elliptic problem; nonlinear boundary conditions; subcritical; Gagliardo-Nirenberg interpolation inequality; L-infinity a priori estimate; EQUATIONS; BIFURCATION;

D O I：

10.1090/proc/17075

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

. We establish an explicit L infinity(Omega) a priori estimate for weak solutions to subcritical elliptic problems with nonlinearity on the boundary, in terms of the powers of their H1(Omega) norms. To prove our result, we combine in a novel way Moser type estimates together with elliptic regularity and Gagliardo-Nirenberg interpolation inequality. We illustrate our result with an application to subcritical problems satisfying Ambrosetti-Rabinowitz condition.

引用

页码：1585 / 1593

页数：9

共 50 条

[21] Mesh-independent a priori bounds for nonlinear elliptic finite difference boundary value problems
McKenna, P. J.
Reichel, W.
Verbitsky, A.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 419 (01) : 496 - 524
[22] AN ELLIPTIC BOUNDARY VALUE PROBLEM WITH FRACTIONAL NONLINEARITY
Abatangelo, Nicola
Cozzi, Matteo
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2021, 53 (03) : 3577 - 3601
[23] A PRIORI ERROR ANALYSIS FOR LINEAR QUADRATIC ELLIPTIC NEUMANN BOUNDARY CONTROL PROBLEMS WITH CONTROL AND STATE CONSTRAINTS
Krumbiegel, K.
Meyer, C.
Roesch, A.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2010, 48 (08) : 5108 - 5142
[24] Bifurcation and asymptotics for elliptic problems with singular nonlinearity
Radulescu, V
Elliptic and Parabolic Problems: A SPECIAL TRIBUTE TO THE WORK OF HAIM BREZIS, 2005, 63 : 389 - 401
[25] A priori estimates of solutions of boundary value problems for two-dimensional systems of singular differential inequalities
Partsvania, Nino
GEORGIAN MATHEMATICAL JOURNAL, 2011, 18 (01) : 163 - 175
[26] Nonlocal semilinear elliptic problems with singular nonlinearity
Youssfi, Ahmed
Mahmoud, Ghoulam Ould Mohamed
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2021, 60 (04)
[27] Anisotropic error estimates for elliptic problems
L. Formaggia
S. Perotto
Numerische Mathematik, 2003, 94 : 67 - 92
[28] Optimal conditions for a priori estimates for semilinear elliptic systems with two components
Li Yuxiang
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (3-4) : 1850 - 1864
[29] Proportionality of Components, Liouville Theorems and a Priori Estimates for Noncooperative Elliptic Systems
Montaru, Alexandre
Sirakov, Boyan
Souplet, Philippe
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2014, 213 (01) : 129 - 169
[30] Anisotropic error estimates for elliptic problems
Formaggia, L
Perotto, S
NUMERISCHE MATHEMATIK, 2003, 94 (01) : 67 - 92

← 1 2 3 4 5 →